Banach Journal of Mathematical Analysis

Completely rank-nonincreasing multilinear maps

Hassan Yousefi

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Abstract

We extend the notion of completely rank-nonincreasing (CRNI) linear maps to include the multilinear maps. We show that a bilinear map on a finite-dimensional vector space on any field is CRNI if and only if it is a skew-compression bilinear map. We also characterize CRNI continuous bilinear maps defined on the set of compact operators.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 2 (2018), 481-496.

Dates
Received: 14 September 2017
Accepted: 29 September 2017
First available in Project Euclid: 7 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1520413214

Digital Object Identifier
doi:10.1215/17358787-2017-0058

Mathematical Reviews number (MathSciNet)
MR3779724

Zentralblatt MATH identifier
06873511

Subjects
Primary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]
Secondary: 47B49: Transformers, preservers (operators on spaces of operators) 47A99: None of the above, but in this section 15A01

Keywords
rank nonincreasing completely rank nonincreasing multilinear maps bilinear maps

Citation

Yousefi, Hassan. Completely rank-nonincreasing multilinear maps. Banach J. Math. Anal. 12 (2018), no. 2, 481--496. doi:10.1215/17358787-2017-0058. https://projecteuclid.org/euclid.bjma/1520413214


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